An Automatic Clustering of Data Points with Alpha and Beta Angles on Apollonius and Subtended Arc Circle based on Computational Geometry

Abstract

Following the recent rapid increase in the amount of information, local recognition of similar and related sets of data points using neighborhood construction algorithms has gained high significance in various fields. In the area of data mining, a main focus of research has been on locating neighborhood construction algorithms. With their high accuracy level in locating highly similar data points and efficient geometric structures, geometric methods have attracted the attention of the scholars since they both reduce time complexities of neighborhood construction and increase grouping accuracy of similar data sets. Due to the significance of the mentioned challenges in data point analysis, geometric method was used in the present study in which Apollonius circle was used to locally extract the concerned target points on the data. In the proposed method, the researchers have no previous knowledge about the data, and having located the similar data sets by the use of Apollonius circle, the direct/indirect relationships inside the circles are studied to boost accuracy in locating neighborhood among the points. The proposed method using Apollonius geometric and subtended arc methods have higher efficiency than the new algorithms on the majority of real data sets.